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摘要翻译：
本文考虑具有滑动平均型时滞生成器的倒向随机微分方程。对线性生成元依赖于$(Y(t),Z(t))$的经典框架进行了扩展，研究了依赖于$(\frac{1}{t}\int_0^ty(s)ds,\frac{1}{t}\int_0^tz(s)ds)$的线性生成元。我们给出了相应的时滞BSDEs的显式解，并详细研究了解的主要性质。给出了处理具有移动平均型时滞发电机的BSDEs的经济动因。我们认为，当我们面对非单调偏好的动态建模问题时，可能会出现这样的方程。我们建立了一个失望效应模型，在此效应下，当前的回报与过去的预期相比较，以及一个波动厌恶效应，该效应导致当前的回报受到过去对波动风险的暴露的惩罚。
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英文标题：
《BSDEs with time-delayed generators of a moving average type with
applications to non-monotone preferences》
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作者：
{\L}ukasz Delong
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最新提交年份：
2011
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
In this paper we consider backward stochastic differential equations with time-delayed generators of a moving average type. The classical framework with linear generators depending on $(Y(t),Z(t))$ is extended and we investigate linear generators depending on $(\frac{1}{t}\int_0^tY(s)ds, \frac{1}{t}\int_0^tZ(s)ds)$. We derive explicit solutions to the corresponding time-delayed BSDEs and we investigate in detail main properties of the solutions. An economic motivation for dealing with the BSDEs with the time-delayed generators of the moving average type is given. We argue that such equations may arise when we face the problem of dynamic modelling of non-monotone preferences. We model a disappointment effect under which the present pay-off is compared with the past expectations and a volatility aversion which causes the present pay-off to be penalized by the past exposures to the volatility risk.
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PDF链接：
https://arxiv.org/pdf/1008.3722
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